The methods currently known for calculating a personalized ablation pattern, which use data coming from wavefront sensors, generally involve mathematical modelling of the optical surface of the eye through series development techniques. More specifically, in order to model the ocular surface polynomials of Zernike polynomials have been used, as proposed by Liang et al., in “Objective Measurement of Wave Aberrations of the Human Eye with the Use of a Harman-Shack Wave-front Sensor”, Journal Optical Society of America, July 1994, vol. 11, No. 7, pp. 1-9, the content of which should be considered entirely incorporated here for reference. The coefficients of the Zernike polynomials are derived from well-known fitting techniques, and the refractive correction procedure is thus determined using the shape of the ocular surface of the eye, as indicated by the mathematical model of the series development.
The methods for reconstructing the surface based on Zernike functions and their accuracy in the case of normal eyes have been studied extensively for regular cornea shapes. See, for example, Schweigerling, J., and Grievenkamp, J. E., “Using corneal height maps and polynomial decomposition to determine corneal aberrations,” Opt. Vis. Sci., Vol. 74, No. 11 (1997) and Gurao, A. and Artal, P., “Corneal wave aberration from videokeratography: Accuracy and limitations of the procedure,” JOSAA, Vol. 17, No. 6 (2000).
Moreover, known modelling techniques are quite indirect, and can lead to unwanted errors in the calculation, as well as a lack of understanding of the physical correction to be made.
Therefore, in light of the above, it is clear that there is a need to be able to have improved methods and systems for mathematically modelling a wavefront.